Of the cultavated swords their are many 100's of different types. the ones that stand out to me is the red eye red's (completely red with red eyes), saw Panda's ay an auction a few weeks back which was a white fish with black fins.
but their far many to list
a google image search would be a quicker option.

Then if you want to know about wild swordtails their many more, some 35 species. Which have different body shapes ans sword lengths.

wagtail swords have a red body and black tail
tuxedo swords have a red front half and black rear section & tail
green swords are the normal wild colour
sunsets are and orange yellow colour
mickey mouse swords came from mickey mouse platies and have the black mouse ears on the caudal penduncle region (just before the tail) and a yellow body
black swords are a black colour (it's closer to a really dark metallic green but some are black these days)
you get one that is pale pink and white but I can't think of what they're called.

If you eliminate the duplicates, the master index of freshwater fish lists 24 wild type xiphophorus. Of that number, we call some swordtails and some platies. Another site lists 20 wild types that they actually name as swordtails. They also list a few as platies. Some of those carry dual common names that include the word platy and swordtail so make your choice of which you want to call them. As helter shelter said, there are probably hundreds of different colors that have been developed by crossings of mostly X helleri (green swords) X variatus (variatus platies) and X maculatus (moon platies). As soon as you think you have a perfect list5 of the manmade crosses and their colors, a new one will come on the market.